Related work.
The Hausdorff distance is a widely used distance metric that can be used for any two subsets of a space. It is a bottleneck measure: only a maximum distance determines the Hausdorff distance.
Efficient algorithms to compute the Hausdorff distance between two simple polygons or their higher-dimensional equivalents exist [1]}, [2]}, [3]}.
The Hausdorff distance is used in computer vision [4]} and computer graphics [5]}, [6]} for template matching, and the computation of error between a model and its simplification.
